My understanding is that the root cause is unmet dependecies of packages grub-efi-amd64 and grub-efi-amd64-signed, so I have tried what is described here How do I resolve unmet dependencies? but the problem still persist.

I'm not sure if the removal of the conflicting packages would fix the issue, but I haven't done it yet as I'm afraid I could ruin my system as it has EFI boot and I'm booting it with GRUB. For the same reason I haven't tried to run sudo apt-get -u dist-upgrade, as perhaps the conflicting packages could be automatically removed.

I'd like to know if others have had a similar experience as well as possible solutions to this.

Just as additional info this is the output of gedit /etc/apt/sources.list:

# deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ dists/precise/main/binary-i386/
# deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ dists/precise/restricted/binary-i386/
# deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ precise main restricted
# See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
# newer versions of the distribution.
deb http://archive.ubuntu.com/ubuntu precise main restricted
## Major bug fix updates produced after the final release of the
## distribution.
deb http://archive.ubuntu.com/ubuntu precise-updates main restricted
## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team. Also, please note that software in universe WILL NOT receive any
## review or updates from the Ubuntu security team.
deb http://archive.ubuntu.com/ubuntu precise universe
deb http://archive.ubuntu.com/ubuntu precise-updates universe
## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team, and may not be under a free licence. Please satisfy yourself as to
## your rights to use the software. Also, please note that software in
## multiverse WILL NOT receive any review or updates from the Ubuntu
## security team.
deb http://archive.ubuntu.com/ubuntu precise multiverse
deb http://archive.ubuntu.com/ubuntu precise-updates multiverse
## N.B. software from this repository may not have been tested as
## extensively as that contained in the main release, although it includes
## newer versions of some applications which may provide useful features.
## Also, please note that software in backports WILL NOT receive any review
## or updates from the Ubuntu security team.
deb http://archive.ubuntu.com/ubuntu precise-security main restricted
deb http://archive.ubuntu.com/ubuntu precise-security universe
deb http://archive.ubuntu.com/ubuntu precise-security multiverse
## Uncomment the following two lines to add software from Canonical's
## 'partner' repository.
## This software is not part of Ubuntu, but is offered by Canonical and the
## respective vendors as a service to Ubuntu users.
deb http://archive.canonical.com/ubuntu precise partner
deb-src http://archive.canonical.com/ubuntu precise partner
## This software is not part of Ubuntu, but is offered by third-party
## developers who want to ship their latest software.
# deb http://extras.ubuntu.com/ubuntu precise main
# deb-src http://extras.ubuntu.com/ubuntu precise main
deb http://archive.canonical.com/ precise partner
deb-src http://archive.canonical.com/ precise partner

And gedit /etc/apt/sources.list.d/* (different files):

deb-src http://ppa.launchpad.net/cassou/emacs/ubuntu precise main
### THIS FILE IS AUTOMATICALLY CONFIGURED ###
# You may comment out this entry, but any other modifications may be lost.
deb http://dl.google.com/linux/chrome/deb/ stable main
### THIS FILE IS AUTOMATICALLY CONFIGURED ###
# You may comment out this entry, but any other modifications may be lost.
deb http://dl.google.com/linux/chrome/deb/ stable main
deb http://ppa.launchpad.net/guilhem-fr/swftools/ubuntu precise main
deb-src http://ppa.launchpad.net/guilhem-fr/swftools/ubuntu precise main
deb-src http://ppa.launchpad.net/rabbitvcs/ppa/ubuntu precise main
deb http://ppa.launchpad.net/yannubuntu/boot-repair/ubuntu precise main
deb-src http://ppa.launchpad.net/yannubuntu/boot-repair/ubuntu precise main
deb http://ppa.launchpad.net/yannubuntu/boot-repair/ubuntu precise main
deb-src http://ppa.launchpad.net/yannubuntu/boot-repair/ubuntu precise main

You seem to have added other repositories to your update manager. try not to add any third party (if your not sure) also untick unsupported updates/ pre-release updates from update manager. check this out for more information google.co.in/…
–
Kanthala RaghuAug 9 '13 at 10:57

I have always had disabled "updates/ pre-release updates" in the update manager. Disabling third party repositories the outcome is the same.
–
Alejandro García SecoAug 9 '13 at 11:14